Skip to main content
Log in

The thermoelastic state of a thermosensitive sphere and space with a spherical cavity subject to complex heat exchange

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

A solution is derived for the non-stationary heat-conduction problem involving a thermosensitive sphere and space with a spherical cavity under convective radial heat exchange with the environment. The influence of the material thermosensitivity on the temperature distribution and the stresses caused by it is analyzed for the cases when force loadings exist and when they are absent on the surface of the bodies considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Beliaiev NM, Riadno AA (1993) Mathematical methods for thermal conductivity. Vyshcha shk, Kyiv (in Russian)

    Google Scholar 

  2. Kolyano YuM (1992) Heat conduction and thermoelasticity method for inhomogeneous body. Naukova dumka, Eyiv (in Russian)

    Google Scholar 

  3. Lomakin VA (1976) Elasticity theory for inhomogeneous bodies. Izd-vo MGU, Moscow (in Russian)

    Google Scholar 

  4. Lykov AV (1967) Heat conduction theory. Vysshaja shkola, Moscow (in Russian)

    Google Scholar 

  5. Postol’nyk YuS, Ogurtzov AP (2002) Metallurgical thermomechanics. Systemni technolohii, Dnipropetrovs’k (in Ukrainian)

    Google Scholar 

  6. Nowinski J (1959) Thermoelastic problem for an isotropic sphere with temperature dependent properties. ZAMP 10(6): 565–575

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. Parida J, Das AK (1970) Note on the thermal stresses in an incompressible non-homogeneous sphere in periodic temperature field. Bull Acad Polon Sci 18: 1–6

    Google Scholar 

  8. Noda N (1986) Thermal stresses in materials with temperature-dependent properties. In: Hetnarski RB (ed) Thermal stresses I, Chap. 6. Elsevier Science, Amsterdam, pp 391–483

  9. Stanišić MM, McKinley RM (1962) The steady-state thermal stress field in an isotropic sphere with temperature-dependent properties. Arch Appl Mech 31(4): 241–249

    Google Scholar 

  10. Nyuko H, Takeuti Y, Noda N (1978) Stationary thermal stresses for a composite hollow sphere exhibiting temperature dependent properties. Trans Jpn Soc Mech Eng 44 (381): 1454–1460

    Google Scholar 

  11. Kolyano YuM, Makhorkin IM (1984) Thermal stresses in a heat-sensitive sphere. J Eng Phys Thermophys 47(5): 1373–1377

    Google Scholar 

  12. Makhorkin IN (1977) Thermal elasticity of a hollow sphere with temperature-dependent thermal conductivity. Strength Mater 9(12): 1441–1442

    Article  Google Scholar 

  13. Bahtui A, Poultangari R, Eslami MR (2007) Thermal and mechanical stresses in thick spheres with an extended FGM model. In Proceedings of the seventh international congress on thermal stresses, vol 2, Taiwan, pp 491–494

  14. Nowinski J (1962) Transient thermoelastic problem for an infinite medium with a spherical cavity exhibiting temperature–dependent properties. J Appl Mech 29: 399–407

    MATH  MathSciNet  Google Scholar 

  15. Popovych VS, Harmatiy HYu (2004) Thermoelastic state of thermosensitive sphere under convective heat exchange with environment. Nauk notatky 15: 252–264 (in Ukrainian)

    Google Scholar 

  16. Popovych VS, Sulym GT (2004) Centrally-symmetric quasi-static thermoelastisity problem for thermosensitive body. Mater Sci 3: 365–375

    Google Scholar 

  17. Popovych VS (1997) Construction of solutions to thermoelastisity problems for thermosensitive bodies under convective-radial heat exchange. Dop NAN Ukraine 11: 69–73 (in Ukrainian)

    Google Scholar 

  18. Carslaw HS, Jaeger JC (1959) Conduction of head in solids. Clarendon, Oxford

    Google Scholar 

  19. Prudnikov AV, Brychkov YuA, Marichev OI (1992) Direct Laplace transforms. Integrals and series, vol 4. Gordon and Breach, New York

    Google Scholar 

  20. Prudnikov AV, Brychkov YuA, Marichev OI (1992) Inverse Laplace transforms. Integrals and series, vol 5. Gordon and Breach, New York

    Google Scholar 

  21. Harmatiy HYu, Kutniv M, Popovych VS (2002) Numerical solution of non-stationary heat conduction problem for thermosensitive bodies under convective heat exchange. Mashynoznavstvo 1(55): 21–25 (in Ukrainian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. M. Kushnir.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kushnir, R.M., Popovych, V.S. & Vovk, O.M. The thermoelastic state of a thermosensitive sphere and space with a spherical cavity subject to complex heat exchange. J Eng Math 61, 357–369 (2008). https://doi.org/10.1007/s10665-008-9214-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10665-008-9214-6

Keywords

Navigation